Get proxies to follow rig generated by manuel bastioni
The problem is that your clothing has no vertex weighting, only empty groups. The solution is to delete the existing vertex groups on the clothing, then transfer the weights from the body. To do this:

1) Select the clothing and put it into weight paint mode.

2) Select the body and put it into weight paint mode as well.

3) While the body is selected, shift+select the clothing. The clothing will now show as selected.

4) Use the Transfer Weights button in the left tool shelf.

5) In the Operator (lower corner of the left tool shelf after you hit transfer weights) make sure that Source Layer is set to By Name, or it will only transfer the active bone/group.

Note that you may wish to hide the rig, as if you have a single bone selected, it may transfer only that bone.

You can also do this with the Data Transfer modifier.